Re: complexity measures etc...

In my program, (more in a moment) I tried a few
complexity measures as part of getting close to
an HE type graph that made sense for me. The
one I keep going back to is simply

c = n*d;
if ( ispowerof2( d ) )
c = c / 2;
return( c );

in other words, the basic product with some fudging
for rootedness. This SEEMS to match the way I hear things,
at least for octave constrained
dyads. (For instance, this ensured that 4:5 was "better"
than 3:4 and 8:9 "better" than 7:8, which seems to match MY
perceptions).

I tried other measures (with help from Paul and others) and
kept finding anamolies that didn't "feel right". Some of
these involved prime factorisation and some calculation
of "distance" and "direction" on the lattice.

The program was an attempt to generate scales via a scale
descriptions (BaBBa as a pentatonic for example) and outputs
them in a suitable order of "goodness", which was loosely
defined as having a few consonant intervals reasonably well
in tune.

This lead me to a bunch of "ear" work and hence abandoning
the program for awhile. Now when I find, by hand and ear, a
scale that seems to have potential I go back and see where
it was on the list of scales generated by the program. The
program isn't completely out to lunch (usually the
things I like are in the top ten) but it still doesn't
seem to understand any better than I do what I'm looking for.

Bob Valentine